I can see what I think might be Daniel’s birth on the LDS pilot site:
Daniel Joseph Murray b Oct – Dec 1882 Dublin South Vol 2 page 646
I think I can see him and his siblings in the censuses, with widowed Mary. If I am right, he had a brother Stephen whose birth appears to be Dub North 1877 Vol 2 p 659. Sister Martha might be Dub N 1874 Vol 17 p 584. Some of the other siblings are not so obvious due to names being more common.
You can order photocopies of these birth certs from GRO in Roscommon. It’ll cost you €4 for each.
www.groireland.ie/ Assuming I have identified the correct events (and you should know that from the mothers name and the addresses etc) you’ll get the elusive father’s name.
Mary Murray was b c 1843 so there’s a chance that her marriage predates the start of stat marriages in Ireland (1864) in which case you should check the parish records for her church to see if you can trace the marriage that way.
I think you should be able to find Daniel’s fathers name. Your real problem may be tracing where he came from in Scotland, especially if you don’t have his father’s name, which may be the case if the marriage was pre 1864.
Elwyn